More than 2 million people have signed up so far for health coverage under Obamacare, officials said Tuesday in trying to put the best face forward before the controversial health care reforms fully kick in with the start of 2014.

The enrollment figure represented a big increase after the botched launch of the system in October, but Health Secretary Kathleen Sebelius was unable to say how many of the 2.1 million who enrolled have paid their first premium to ensure their policies take effect on Wednesday.

Sebelius and other officials also acknowledged the possibility of more potential problems, warning people to bring proof of coverage with them to their doctor or pharmacy, pay premiums when due and double-check with insurers that they are covered.

Under the reforms, Americans will be required to have health coverage or face a fine. Sebelius called the full implementation of reforms under the 2010 Affordable Care Act a new era in health insurance, noting they mean no denial of coverage for pre-existing conditions or other discriminatory practices such as charging women more than men.

"Starting tomorrow, being a woman will no longer be a pre-existing condition," Sebelius said on a conference call with journalists.

The Obamacare enrollment figure is below the target of 3 million originally set by the administration for the end of December, which is halfway through an initial six-month sign-up period under the law intended to help millions of previously uninsured Americans get coverage.

Overall, the administration hopes to enroll 7 million people by March 31 while also expanding eligibilty for Medicaid, the government health care program for the impoverished.

Sebelius said Tuesday that another 3.9 million people were eligible for coverage through expanded Medicaid and Children's Health Insurance Program, but she was unable to specify how many have become new enrollees.

The botched rollout of the new marketplaces on October 1, when the HealthCare.gov website set up to handle the enrollment failed to work properly, damaged the sign-up process until the system began working better in early December.

Sebelius said the administration was "doing everything we can to help ensure a smooth transition period" for people getting new coverage.

Anticipating possible problems in the enrollment system, Sebelius also advised in her blog post that "if you thought you enrolled in health coverage but aren't showing up in the system, call your insurance company directly."

She also said people could contact the Obamacare call center for assistance.

Asked if the website woes in October and November could be due to attacks from outside by Obamacare opponents, a spokeswoman for the Centers for Medicare and Medicaid Services told reporters there were technological problems but no sign of hacking.

The health care reforms championed by President Barack Obama have become the defining issue of his presidency, with Republicans led by tea party conservatives trying to dismantle them while some Democrats appearing leery of campaigning on them in the November congressional elections.

While the Supreme Court ruled the mandate to obtain health coverage was constitutional, further legal challenges are being mounted.

Also on Tuesday, a group of Catholic organizations, in an emergency appeal, asked the Supreme Court to delay the Obamacare requirement that certain religious-affiliated groups provide contraception and "abortion-inducing drug" coverage to their workers.

Archdioceses in Washington, D.C., Tennessee and Michigan -- along with affiliated groups that include Catholic University -- asked Chief Justice John Roberts and Justice Elena Kagan to block enforcement of the related employer mandates set to take effect on Wednesday.

The issue has been a major sticking sticking point with religious groups and private for-profit companies that have strong moral objections.

The Supreme Court agreed last month to hear two cases involving for-profit corporations who say their religious liberty is violated by the law.